We will start by discussing the thermodynamic limit of such a model and how integrability impacts the properties of its stationary states. To that end we will rely on the celebrated Thermodynamic Bethe Ansatz (TBA). This was initially developed to specifically deal with the Lieb-Liniger model [1]}, but it turns out that its applications are significantly more far-reaching [2]}. We will then use these results to construct a hydrodynamic theory of integrable systems according to [3]}. As we shall see in the next section, parallels are to be drawn between quantum particles and solitons.
